Abstract We propose a method to deform robot trajectories based on affine transformations. At the heart of our approach is the concept of affine invariance: trajectories are deformed in order to avoid unexpected obstacles or to attain new goals but, at the same time, certain precise features of the original motions are preserved. Such features include for instance trajectory smoothness, periodicity, affine velocity, or more generally, all affine-invariant features, which are of particular importance in humancentered applications. Furthermore, the proposed method is very efficient and easy to implement: there is no need to re-integrate even a part of the trajectory and, in most cases, closed-form solutions can be worked out. The method is also versatile: optimization of geometric and dynamics parameters or satisfaction of inequality constraints can be taken into account in a very natural way. As illustration, we present a method for transferring human motions to humanoid robots while preserving equiaffine velocity. Building on the presented affine deformation framework, we finally revisit the concept of trajectory redundancy from the viewpoint of group theory.